TY - JOUR
T1 - Stochastic tamed 3D Navier-Stokes equations
T2 - Existence, uniqueness and ergodicity
AU - Röckner, Michael
AU - Zhang, Xicheng
PY - 2009/9
Y1 - 2009/9
N2 - In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly (Ann. Math. 164:993-1032, 2006), we prove the uniqueness of invariant measures for the corresponding transition semigroup.
AB - In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly (Ann. Math. 164:993-1032, 2006), we prove the uniqueness of invariant measures for the corresponding transition semigroup.
KW - Asymptotic strong Feller property
KW - Ergodicity
KW - Invariant measure
KW - Navier-Stokes equation
UR - http://www.scopus.com/inward/record.url?scp=67649125135&partnerID=8YFLogxK
U2 - 10.1007/s00440-008-0167-5
DO - 10.1007/s00440-008-0167-5
M3 - Article
AN - SCOPUS:67649125135
SN - 0178-8051
VL - 145
SP - 211
EP - 267
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 1-2
ER -